slope & y-intercept Edited version of kballard @ math.weebly.com

Vocabulary A rate of change is a ratio that compares the amount of change of a dependent variable to the independent variable. Slope: the steepness of a line described by rate of change of y and x.

Steepness of Lines The slope of a line is a measure of its steepness. Use absolute value to compare the steepness of multiple lines.

What is slope?

What does slope look like? There are four types of slope that describe the rate of change. Using this will help you check your work and describe your linear equation.

Slope Formula If you do not have a graph, but want to find the slope, you can use two points in the slope formula. Substitute in both points Subtract and simplify

y = mx + b Slope-Intercept Form The linear equation y = mx + b is written in slope-intercept form. x and y stand for any x and y value. m is the slope (rise over run) b is the y-intercept (on the y-axis) y = mx + b

Identify slope and y-intercept y = 4x + 5 y = ½ x – 7 y = x – ¾ y = -x + 3 y = x y = 4 x = 2 y= mx + b m is always slope b is always the y-intercept Look at each equation and determine the slope value and the y-intercept value.

Identify slope and y-intercept y = mx + b If you have the graph, Find the y-intercept Count rise over run Write the equation

Write the linear equation. Write the equation in slope-intercept form. y = mx + b

Graphing a line. Slope-intercept form is the easiest way to graph a line when you have an equation. It is the main way that lines are expressed. Y = x + 2

Examples

Describing Slope -EX Tell whether the slope of each line is positive, negative, zero, or undefined.

Finding Slope from a Graph-Ex To find the slope from a graph, Pick any two points on the line. Count RISE over RUN and simplify

Practice Name the type of slope and find the slope.

Special Cases

Practice Find the slope of each line.

Slope Formula-EX

Practice

Graph Lines #1 How will we graph a line when we have y=mx + b? Example: y = 2/3x - 4 m= _____ b = _______ Plot the y-intercept Use your slope to count rise over run Connect the dots!

Graph Lines #2 How will we graph a line when we have y=mx + b? Example: y = -3x + 2 m= _____ b = _______ Plot the y-intercept Use your slope to count rise over run Connect the dots!

Graph Lines #3 How will we graph a line when we have y=mx + b? Example: y = 1 m= _____ b = _______ Plot the y-intercept Use your slope to count rise over run Connect the dots!

Graph Lines #4 How will we graph a line when we have y=mx + b? Example: x = -3 m= _____ b = _______ Plot the y-intercept Use your slope to count rise over run Connect the dots!

Graph Lines Identify the slope and y-intercept, then graph the linear equation. y = 2x + 3 y = -½x - 1 y = 5/6x + 8 y = x - 7

REVIEW What is rate of change? What is slope? What are the four types of slope? What does “rise” represent? What does “run” represent? How do you find slope from a graph? What is the slope formula?

Review What is slope-intercept form? What do m and b represent? How do you graph a line with slope-intercept form? What are the two special cases?

MATH HUMOR How are linear functions similar to Cupid? They have a partner for every number. Teacher: Where’s the graph of your function? Student: It was intercepted on the way to school. Why were the math students getting up and sprinting around the classroom? Their teacher kept saing “rise” and “run” Why was the scientist smiling as he worked? His graph had a great plot!